Hungarian uprising: 50 years

Today, it's been exactly half a century since the beginning of the

• Hungarian revolution in 1956,

the most important uprising in Hungary since the anti-Habsburg revolution of 1848. Decades later, October 23rd became the Hungarian national holiday. Congratulations to all Hungarian readers.

Much like other revolutions including the Czechoslovak Velvet Revolution in 1989, it was started by students. Students who loved freedom. Students who wanted the public radio to broadcast their demands - such as freedom and the removal of a Stalin's statue built on the place of a church ;-) - but who were instantly arrested, sparking a truly national movement.

A week later, the Soviet army stopped the uprising and killed 2,500 people or so while it lost 700 soldiers or secret policemen. 13,000 civilians were wounded and the moderate communist leader Imre Nagy was among the 350 citizens who were executed. About 200,000 Hungarians fled the country as refugees.

The action of the communists was so disgraceful that 700,000 out of 800,000 members of the Hungarian communist party canceled their membership within a month or so. That couldn't stop János Kádár, the newly installed leader, to gain a full control over the country. I suspect that this experience showing the Hungarians that communism can be really evil was one of the reasons why Hungary became an example of the moderate "goulash socialism" in the 1980s. Twenty years ago or so, we would visit Hungary that exhibited a sort of a mixed economic system. Mikhail Gorbachev became the first Soviet leader who apologized for the intervention.

From a strategic viewpoint, it was obvious that the communists - including the Soviet ones - had to suppress this uprising if they wanted their favorite regime to have a chance to survive in the long term. They had all the necessary requisites to do so. The message was also rather clear for the Czechoslovak reformers during the Prague Spring of 1968: it is useless to fight against the Soviet Union. Give it up. Well, I don't want to claim that the Czechoslovaks would fight if there had been no bloody experience with the Hungarian uprising but who knows. ;-)

The suppression of the Hungarian revolution has had many international consequences. The Time magazine declared the Hungarian freedom fighter to be the Man of 1956. More importantly, the Western European communist parties were divided. Most of their members and leaders considered the revolutionaries to be a reactionary mob: however not all of them.

Some people who love freedom will always be born. The defenders of communism and other totalitarian ideologies face a choice: either they allow freedom which means that they allow their favorite system to be marginalized and to evaporate, or they impose tough rules that eliminate all the people who actively prefer freedom over these rules. Most communists are able to solve elementary exercises in strategy which is why they choose the second option. Communism and every other extreme left-wing or extreme right-wing ideology that wants to mold the society according to a template is an unhuman monstrosity, and if it is not an unhuman monstrosity, it cannot be an extreme left-wing or extreme right-wing ideology with plans about the whole society.

The United Nations have passed a resolution that the intervention had violated the human rights of the Hungarian people and that was it. The United Nations were as useless in these important matters 50 years ago as they are useless today. Albert Camus wrote a letter protesting against the West's inaction but the power of a single Camus's letter has its limitations.

Today, we often want to complain that Iraq is a mess, and all these things. I still feel that these problems are less serious than the problems that the world had to swallow 50 years ago. Today, the Hungarian society seems sharply divided politically. Still, the divisions seem less bloody than the divisions that existed 50 years ago.

Despite the divisions, nearly everyone seems to agree: the freedom fighters in 1956 were heroes.

And that's the memo.

The temptation of rigor

Jacques Distler wrote a nice text about

• the role of rigor

in physics. He explains that rigor can't replace physical input and insights: very rigorous theorems may lead to very misleading physical conclusions. A reader could ask: how could a physicist ever question the unlimited power of a rigorous proof of a mathematical theorem? The technical answer is hidden in the assumptions of the theorem.

A proof of a theorem can be completely correct but the theorem can still be physically worthless. This occurs when the assumptions of the theorem are not satisfied by the relevant physical systems. When you start with incorrect or naive assumptions, your reasoning is likely to follow the GIGO rule: garbage in, garbage out. Rigor simply can't save you from errors in physical reasoning. There exists no systematic or rigorous method to find the correct physical theories.

Jacques mentions two examples:

1. algebraic holography
2. uniqueness of the polymer representation of the spatial diffeomorphism constraints

In both cases, rigorous proofs about systems called "quantum field theory" or "quantum gravity" have been constructed. These theorems are proven by valid proofs so what's the problem? The problem is that it is misleading to use the terms "quantum field theory" and "quantum gravity" for the theories addressed by these theorems.

In the case of algebraic holography, a rigorous proof due to Karl-Henning Rehren may be given to show that a local "quantum field theory in d+1-dimensional anti de Sitter space" is equivalent to a local "quantum field theory defined on its d-dimensional boundary". In this case, the definition of a "quantum field theory in d dimensions" is far too loose and includes structures that a physicist would never count as quantum field theories in d dimensions.

For example, a four-dimensional interacting Klein-Gordon theory can be included among three-dimensional quantum field theories according to this definition because the field "phi(x,y,z,t)" can be written as "phi_z(x,y,t)" with an index "z". There are many good reasons why continuous indices for fields are never treated as indices by the physicists and why the theoretical physicists would declare the conclusion of the theorem to be manifestly incorrect physically: local theories in d dimensions have free energy density that scales like "T^d" for high temperatures "T"; theories in different dimensions therefore can't be equivalent because you can always determine the dimension from the exponent.

However, with the unusual definitions of quantum field theories and their dimensionality used in the theorem, it is not surprising that one can prove a statement that sounds like Maldacena's correspondence. But in reality, it has nothing to do with the real essence of holography in quantum gravity. The theories discussed by algebraic holography are not holographic in any useful sense and they cannot be equivalent to lower-dimensional theories as long as you compute the spacetime dimension of a theory as the physicists do.

The second example - the polymer representations - is analogous but in some sense it suffers from the opposite flaw. In this case, the definition of "quantum gravity" is too narrow-minded. Too many things are assumed to be true about the structure that is called "quantum gravity": it is essentially assumed that quantum gravity must be constructed in the most naive way one can imagine.

These assumptions seem to be invalidated in the actual working theories of quantum gravity because of many unexpected twists and turns. For example, the definition of quantum gravity in terms of the dual CFT directly constructs the physical Hilbert space of quantum gravity - a superselection sector of string theory - without any intermediate steps where the diffeomorphism constraints would have to be imposed by hand. In this construction, a whole dimension of space - the holographic dimension - emerges unexpectedly: it was not used as a starting point at all. Still, all the facts that are normally derived as consequences of the diffeomorphism symmetry hold in this setup.

On the other hand, the polymer theorem is based on the assumption that neither of these "miracles" ever occurs. But these miracles and many other miracles that would be shocking for the thinkers in 2000 B.C. and other thinkers in the past have been found and they represent what we really mean by progress in science. The expectation that we already know all the right assumptions in physics is equivalent to the expectation that there will no longer be any substantial progress in the research of a given class of questions. This expectation is usually incorrect although it is valid whenever someone is smart and lucky enough to find the right assumptions.

The physical conclusion is obvious: Maldacena's correspondence is highly non-trivial, fascinating, and true - it is even more fascinating because rather reasonably sounding but naive and flawed arguments could lead us to believe, together with Roger Penrose, that it can't be right. And in some sense, quantum gravity and holography as painted by string theory is so valuable not only despite but because the structure is so rich that we can't yet fully squeeze these ideas into a small mobile rigorous box that is fully understood.

The fact that we don't yet know everything about string theory and its universal definition is actually one of the reasons why people can't resist and they continue to study it.

On the other hand, algebraic holography and polymer representations of quantum gravity are not so interesting because what is hiding in these fancy rigorous clothes is a physically flawed content that has nothing to do with the important principles of observable physics that are incorporated in the state-of-the-art theories. It's a content that has no relations with the actual surprises that we learned in the recent decades, centuries, and millenia. This content can perhaps be fully understood and the science behind it is falsifiable. Indeed, it is falsifiable in less than an hour. But it is a huge disadvantage, not an advantage, of such a system of ideas.

Rigor can sometimes be useful for physics, especially when physicists are making an error that is caused by a somewhat sloppy reasoning. But the physicists typically reach the right conclusions without insisting on all the formal features of a rigorous proof: they prefer the content over the form. If someone prefers the form over content, it doesn't save him or her from deep physical errors or from naivite. That's why we have so many examples of pairs of answers among which the more rigorous one is obviously the wrong one physically.

The previous articles related to the relation of rigor and physics:

• Category theory and physics
• Bert Schroer's paper
• Algebraic quantum field theory
• Platonic world of mathematical ideas
• Defense of the path integrals
• Physics and mathematics: boundaries and interactions
• Roger Penrose and holography